Assignment 1 Due Date: 24 August 2016 Value : 200 of the 1000 total marks for this course QUESTION 1 The segment of shaft shown in Figure 1 is made of AISI 1095 annealed steel. The shaft is fine turned with a diameter of D=20 mm and with a transverse hole of d=3 mm diameter. The segment as shown is part of a drive shaft for a mixing machine. Under normal operating conditions the shaft segment rotates at 60 rpm and is subject to the following fluctuating loads:  A torque that varies from -120 Nm to +120 Nm once every five seconds;  An axial tensile load that varies from 0 to 8 kN at the same rate as the torque variation; and  A bending moment that varies between 10 Nm and 40 Nm once every second. Determine the expected life of this segment of shaft. (If you determine life in excess of the Endurance limit then determine the factor of safety). [100 marks] Figure 1. Shaft segment Question 1 QUESTION 1 1 1QUESTION 2 Figure 2. Pressure vessel end-cap The end-cap of a pressure vessel as shown in Figure 2 is secured by 10 off M12 x SAE class 8.8 bolts (with rolled threads). A soft gasket is used such that the clamped member stiffness is one third of the bolt stiffness. The internal diameter of the pressure vessel is 300 mm and the pressure in the vessel varies from 0 to P kPa gauge. Assuming that the bolts are initially tightened to 80% of their yield strength determine : (a) the maximum value of P that would not cause separation of the joint; (b) the maximum value of P that would not cause eventual fatigue failure of the bolts; and (c) the wall thickness required for the pressure vessel for this maximum pressure P. [100 marks] QUESTION 2 2MEC2401 – Dynamics 1 S2, 2016 1 University of Southern Queensland Faculty of Health, Engineering and Sciences Assignment 1 Due Date: 29th August 2016 Value: 100 of 1000 total marks for this course Notes: Assignment must be submitted electronically and students should follow the assignment guidance given in the file "instructions for assignment preparation'' which is posted on the course study- desk Q1. (Marks 20/100) A particle is projected to the right from the position x = 0 with an initial velocity 9m/s. if the acceleration of the particle is defined by the relation a = −0.6 v3/2 where a and v are expressed in m/s2 and m/s, respectively. Determine 1. The distance the particle will have travelled when its velocity is 4m/s. (8 marks) 2. The time when v = 1m/s (6 marks) 3. The time required for the particle to travel to 6m (6 marks) QUESTION 3 Q 3MEC2401 – Dynamics 1 S2, 2016 2 Q2. (Marks 25/100) At a given instant in an airplane race, airplane A is flying horizontally in a straight line, and its speed is being increased at the rate of 8m/s2. Airplane B is flying at the same altitude as airplane A and, as it rounds a pylon, is following a circular path of 300 m radius. Knowing that at the given instant the speed of B is being decreased at the rate of 3m/s2. Determine, for the position shown in Figure Q2 1. The velocity of B relative to A (10 marks) 2. The acceleration of B relative to A (15 marks ) Figure Q2 450 km/h 540 km/h 400 m 30o 300 m QUESTION 4 4MEC2401 – Dynamics 1 S2, 2016 3 Q3. (Marks 35/100) The motion of rod OA about O is defined by the relation θ = F(t), where θ and t are expressed in radian and second, respectively. Collar B slides along the rod so that its distance from O is r = G(t) , where r and t are expressed in dm and second, respectively. When t = 1s determine 1. The velocity of the collar, (10 marks : 5(A) + 5(B)) 2. The total acceleration of the collar , (10 marks: 5(A) + 5(B)) 3. The acceleration of the collar relative to the rod (10 marks: 5(A) + 5(B)) In the two following cases A. � = �(�) = �(4�2 − 8�) ; � = �(�) = 10 + sin �� B. � = �(�) = 2 � sin �� ; � = �(�) = 25 �+4 4. Use a software/programing language you know to draw the trajectory of the collar relative to O (5 marks) Figure Q3 QUESTION 5 5MEC2401 – Dynamics 1 S2, 2016 4 Q4. (Marks 20/100) The system shown in Figure Q4 starts from the rest, and the length of the upper cord is adjusted so that A, B, and C are initially at the same level. Each component moves with a constant acceleration, and after 2 s the relative change in position of block C with respect to block A is 280 mm upward. Knowing that when the relative velocity of collar B with respect to block A is 80 mm/s downward, the displacement of A and B are 160mm downward and 320mm downward, respectively. Determine 1. The accelerations of A and B if �� > 10��/�2 (10 marks) 2. The change in position of block D when the velocity of block C is 600 mm/s upward (10 marks) Figure Q4 QUESTION 6 6